The Discipline Review of Teacher Education in Mathematics and Science (Department of Education, Employment and Training, 1989) noted that there was a mismatch in many cases between what was taught in teacher education courses and what subsequently evolved in primary school classrooms. Teacher education courses do not appear to be effective in changing the traditional beliefs and images about teachers and teaching that students bring to their pre-service education (Calderhead & Robson, 1991; Kagan, 1992; McDaniel, 1991; Weinstein, 1990). For example, within mathematics education, Lerman (1983, 1990) and Thompson (1984) showed that teachers’ instructional practices were closely related to their beliefs about mathematics. In addition to the influence of prior beliefs, beginning teachers undergo the transition from university study to fulltime classroom practice with little practical professional experience. They have relatively few weeks of student teaching and often have unrealistic personal performance expectations when they begin fulltime teaching and the associated total responsibility for programming and lesson planning, instruction, motivation, classroom management, assessment, and reporting to and interacting with parents (Johnson, Ratsoy, Holdaway & Friesen, 1993). Hence, many beginning teachers’ preliminary experiences are as a form of ‘survival’ within the classroom, and in this context there is a constant interplay between situational constraints and individual choices or desires (Katz, 1972; Zeichner, 1983). The social context or ‘cultural milieux’ (Taylor, 1996), therefore, exerts considerable influence on day-to-day happenings, interactions, and teaching and curriculum decisions. Further, within this process of ‘teacher socialisation’ (Zeichner, 1983), the children in the classroom along with the school, other staff members, the community, and society in general can all impact upon a beginning teacher’s decisions and pedagogical practices.

These belief, social and contextual factors that the literature reports as influential components of teaching practices, along with the apparent mismatch between teacher education programs and subsequent teaching practices, were the motivation for the study upon which this paper is based. The overall study (Sparrow, 2000) aimed to examine three main things:

This study was informed and conceptualised within three main frameworks within current literature in teacher education: (i) constructivist learning theory, (ii) stages and foci of teacher development, and (iii) ‘fellow worker’ professional development support. Key features of each of these frameworks are outlined next, with particular attention upon how each relates to the design and foci of the study.

Constructivism has been embraced by many teacher educators around the world as a learning theory that provides avenues by which to promote learning with understanding (Klein, 1999). From a constructivist perspective, learning is a result of one’s construction of knowledge through active cognitive and social engagement in one’s experiential world (von Glasersfeld, 1991, 1995). This engagement involves individual interpretations of, and reflection upon, physical and mental activity so that one creates viable and adaptable cognitive schemata and ways of acting in the world (Wood, 1995). The pedagogical implications of constructivism are that teachers should act as facilitators who provide appropriate activities and support for students to personally construct meanings, rather than receive them ready-made from the teacher (von Glasersfeld, 1995). Classroom environments should therefore encourage creativity, problem solving, exploration and sharing of ideas.

In the context of a teacher education classroom this would include a focus on construction of knowledge of how children learn, and in the context of this study the focus would be upon mathematics learning. The teacher education program in which the teachers in this study had participated was framed by constructivist principles. Within the mathematics components of these studies, emphasis was placed on constructing knowledge of teaching and learning activities that foster children’s exploration of mathematical concepts and processes through the use of concrete objects, real world experiences and discussion.

During their teacher education course, all teachers in the study were involved in discussion relating to major models of learning. They would discuss teacher-centred models of learning where the teacher controls what is to be transmitted or imparted to all children in the class. For example, within the context of mathematics, this might be a standard procedure for calculation or a list of names for shapes. This model would be compared, evaluated, and contrasted with a learner-focused approach where students are assessed to establish what they know. From this the teacher plans the next phase of learning. Within this model students are placed in problem situations relevant to their learning needs. The teacher guides them through the next aspect of learning by means of questions rather than direct instruction.

Recognising that, according to the literature, if teachers are to teach mathematics in a constructivist manner then they must hold beliefs about mathematics teaching and learning compatible with this perspective (Raymond, 1997), this study was specifically designed to include examination of teachers’ beliefs. It is generally agreed that the relationships between beliefs and classroom practices are complex, and are influenced by a range of cognitive, psychological and social factors (Cooney, Shealy & Arvold, 1998; Raymond, 1997), the nature of the links is not yet well understood. Hence, this study was designed to contribute to knowledge in this field.

In examination of student teachers’ progress from novice to professional, Furlong and Maynard (1995) articulated a framework of stages or expanding domains that guide the foci of growth as a teacher. These stages or domains have been interpreted by Frid, Reading and Redden (1998) as the model outlined in Figure 1.

The ‘fellow worker’ model for professional development was designed from key characteristics of effective teacher support identified in the literature (Sparrow, 2000). Within the literature two main themes emerged. First of these was the importance of helping teachers to become reflective professionals who continue to learn and change in thoughtful ways. This change requires ongoing reflection on underlying assumptions about teaching and learning, along with examination of practices. Since learning to teach is a life-long endeavour, change needs to be seen as an ongoing continual process (Borko & Putnam, 1998; Gratch, 1998). Pathways by which to support change emerged as the second theme, and specifically, the value of learning communities. Learning communities can play a role as support mechanisms, and also can act as catalysts to initiate and then foster reflection.

Essential features of the ‘fellow worker’ professional development model of this study were developed with these key themes in mind. These features focused upon teachers: (i) constructing their own knowledge base, (ii) reflecting and experimenting in relation to their professional practice, (iii) talking with other teachers to share with and support each other, and (iv) being empowered to decide upon issues for attention and action. The ‘fellow worker’ model was based on the earlier work of Feiman-Nemser (1992) and Clarke (1996). This person became a hybrid of critical friend, colleague, listener, mentor, resource support and interested person. He was not part of the school or the employing authority, and hence, did not perform an assessment function with regard to the teachers’ performance. Since a purpose of the role of the ‘fellow worker’ as conceived in this study was to help the beginning teachers make their ideas personal and exposed, the study was designed to provide opportunities for them to reason about and learn from their own teaching experiences. In this context it was recognised that, as Easen (1985) noted:

Consequently, the ‘fellow worker’ had to be more concerned with choice than with change, and be wary of reinforcing his self-image irrespective of the needs and wishes of the beginning teachers. At the same time he could not be too ‘laissez-faire’ and allow an ‘anything-will-do’ attitude.

Three of the beginning teachers (Stephanie, Tiffany, and Gaz) gained fulltime placements in government primary schools, while the fourth (Harry) was employed at a small Christian school for four days per week. All four schools were small or mid-sized, consisting of principal and four to seven fulltime teachers. The schools were located in low to middle socio-economic areas. Three schools were in outer metropolitan areas of Perth, while the fourth (Tiffany’s school) was in a country town about two hours drive from the city. All four teachers were assigned to multi-aged classes. Stephanie had a class of Years 5 and 6 students Tiffany and Gaz each had Years 2 and 3, and Harry had a class of Years 5, 6, and 7.

Data were collected from interviews, teacher and researcher journals, group meetings, and classroom observations. Interviews occurred at least twice each term, while group meetings took place at the end of each of Terms 1, 2, and 3. The ‘fellow worker’ (author 1) was the interviewer. Interview transcripts were the initial data analysed, with the other data sources used to substantiate and expand themes identified in the interview data. Hence, data analyses proceeded inductively, with NUD*IST as a data handling tool (Qualitative Solutions & Research, 1997). Initial nodes for use in NUD*IST were selected from factors identified from the literature as relevant influences upon pedagogy. The recurring themes and emerging issues that were identified were generally related to the teachers’ overall teaching contexts, not just their mathematics teaching. Hence, in upcoming sections of this paper, the discussions will indicate when the themes and issues were specific to mathematics teaching.

During their first year of teaching the participants in this study faced many challenges with regard to both unique and common features of their teaching situations and related pedagogical beliefs and actions. The recurring themes that appeared early on, as well as the emerging issues, reflected the complexities of teaching situations and how pedagogical beliefs and practices are influenced by a variety of inter-related factors. The nature and role of each of these factors are outlined in upcoming sections and explicated along with examples from the case study situations and related interviews. They are discussed separately, yet are in fact related in complex ways that can only be partially examined in this investigation. Changes throughout the year in the ways teachers dealt with the recurring themes and emerging issues are noted, particularly as they related to the influence of the ‘fellow worker’.

The recurring themes that became apparent early in the year related primarily to the first research question. That is, they were factors that early in the year impacted upon pedagogical practices, and then continued to influence these practices. They included: classroom control, coverage of the required syllabus within the time allotted, teaching mixed ability classes, and assessing what children know.

Control, as a theme, recurred in conversations with the teachers throughout the year, and was particularly notable during the first two terms. The teachers had all had experience as student teachers for the day-to-day responsibility of running of a class, yet the move to managing their own class proved to be a ‘reality shock’. They found ‘control’ difficult, they worried about it, and it dominated the factors they considered when planning for and conducting lessons. As a consequence, they adopted a pedagogical style that could be described as traditional and teacher-centred. For example, within mathematics, lessons were focused on facts and procedures, and were controlled by the teacher working at board. The students’ participation involved working from a textbook, worksheet, or blackline master. For example, Tiffany noted that:

As with Tiffany, the teachers explicitly noted that they chose a teacher-centred approach as a way of controlling students’ behaviour, since students would then have no reason to talk, walk about the classroom, or interact with peers. This would ensure the classroom would be quiet and orderly, with students all working on a task – features of what they believed others see as ‘good’ teaching. These ‘others’ included colleagues, the principal and parents. In fact, there was a perception in the group, especially Harry, that they had to prove quickly that they were good teachers, and ‘good’ in this regard included a controlled class.

Although the teachers’ pedagogical practices were predominantly teacher-centred as a result of their worries about control and their beliefs that it was important to have a controlled classroom, they did sometimes warily try other approaches. For example, Gaz introduced games as a mathematics activity, and Harry and Tiffany tried using concrete materials for hands-on mathematics activities. These approaches put a strain on the control aspects of the class that for Harry and Tiffany led to abandonment of the more leaner-centred strategies. However, Gaz, in spite of the increased noise and apparent chaos, chose to continue with using games, noting that he saw student motivation and better learning as an eventual outcome.

There was some evidence, however, that as the year progressed and the teachers became more confident in their abilities to manage the children, they began to consider alternative teaching approaches. The role of the ‘fellow worker’ appeared influential in this regard, as he was able to offer ideas and resources as well as emotional support. The teachers needed small successes with new endeavours for them to persist in implementing them. For example, Stephanie wanted her students to work in small groups to promote talking about mathematics and discussing ideas, but abandoned such an approach early in the year when it led to ‘control’ problems. Later, when she became less concerned with control she began to change her practices:

This influence of the ‘fellow worker’ to encourage reflection on one’s teaching and subsequent risk-taking will be examined further in upcoming sections of this paper.

All the teachers frequently mentioned coverage of the syllabus in a specified timeframe as a major factor affecting their teaching, and in particular, that there was "never enough time" to do all the planning and teaching needed. There was not enough time to plan detailed, interesting activities, and there was not enough time overall on a day-to-day basis to cover all the syllabus:

Using a traditional textbook or worksheet approach to mathematics teaching allowed lesson planning to be completed quickly and easily, and it allowed for teaching to proceed within a planned timeframe. If the textbook or worksheet tasks were not completed in that timeframe, they could be finished at home. In that way, all the students could keep up and the teacher could the next day move onto the next stage or page of the textbook. More open-ended or discussion-based activities were seen to take longer to both plan and implement, so they were not seen as viable options because less work and syllabus content would be covered.

Noted already, an anxiety early in the year for the beginning teachers was to be seen by others as a ‘good’ teacher. Part of their vision of a ‘good’ teacher involved making sure they could say the students had been taught everything in the syllabus for that year. The extreme nature of their concerns in this regard is reflected in the actions they undertook to ensure syllabus coverage. For example, Stephanie geared her planning to make sure everything was ticked off on a scope and sequence chart, and Harry put such focus onto covering the required mathematics content that he had completed it all by the end of Term Two:

Within this ‘cover the syllabus’ approach, each piece of the syllabus received one lesson, with the subsequent lesson commencing on the next piece. Hence, the emphasis was upon ‘taught’ coverage rather than ‘learned’ coverage. Gaz was the only beginning teacher to recognise and value early in the year that more time than one lesson was needed for each piece of learning for his class. For Stephanie and Tiffany, this awareness did not come until Term Four. Then, they began to relax about the need for syllabus coverage, instead focusing upon the quality and depth of students’ actual learning and implicitly discarding the assumption that if something is taught it is automatically learned by the students.

Finding a balance between student learning and the pressures of syllabus coverage did however remain a dilemma:

As a recurring theme, this challenge was closely related to a recognition of the diverse capabilities within classes, the theme discussed next.

All the teachers had multi-aged groupings in their classes, in addition to the usual mixed ability levels to be found within any class. To deal with this diversity was a concern for them throughout the year because they acknowledged early on that they did not have the pedagogical knowledge or experience to deal with the diversities:

The initial ways the teachers handled these challenges altered little throughout the year. For the most part, they adopted a traditional textbook approach to teaching in which students were matched to the textbook for their year level, allowing for the different year levels to work at what were perceived to be appropriate activities for that part of the syllabus. Within the year levels, the teachers aimed to ‘teach to the middle’, followed by spending more time during seat work with weaker students. The more capable students were not given anything that more closely matched their achievement levels, and were given additional, trivial, or busy work if they completed the work assignments early:

Hence, the teachers’ pedagogical practices did not cater for mixed ability classes. Instead, they aimed to keep the overall groups together. It was not seen as appropriate to let capable students "race ahead" with course work while "the children who are way behind … stay that far behind all the way along" (Harry; journal). However, there was a growing recognition that "where children were at" (Tiffany) is important. Knowing where they are at is an assessment issue, the focus of the next section.

All the teachers showed concerns about their lack of skill in identifying what the students knew, in relation to prior knowledge as well as a result of recent teaching. They entered the year feeling they did not know what students of a particular year level could do, and they also felt they lacked information about their specific students. However, they did not seem able to use strategies that might help them ‘tune into’ what students knew. For example, when it was suggested to Stephanie and Tiffany by the ‘fellow worker’ that they might use a pre-teaching oral or written task to find out what the students knew, they responded enthusiastically to the idea, but then made no attempt to implement it. Similarly, they did not act upon discussions early in the year with the ‘fellow worker’ about alternative forms of assessment to pencil and paper tests such as portfolios, journal writing, or performance tasks.

It appeared that the teachers did not see these learner-focused assessment strategies as viable within their situations because they gave "information in a form you can’t use or know how to use" (Stephanie). A consequence of adoption of a traditional textbook approach to mathematics instruction was that teaching emphasised facts, procedures, and calculations. This in turn led to using traditional pencil and paper tests for assessment. Tests were quicker to plan and administer, and did not require working in unfamiliar and less controlled styles.

However, later in the year, the teachers began to experiment with alternative forms of assessment. Stephanie began to use portfolios and simple writing journals, Tiffany and Harry began to work with observation schedules, and Gaz incorporated work samples and oral accounts from children. Thus, the teachers’ assessment pedagogies began to shift alongside changes in their teaching styles. Often these changes in practice were first initiated after discussions with the fellow worker:

This interview extract highlights the importance that reflection played in initiatives to try new things or change pedagogical practices. The fellow worker, as a "sounding board", was able to provide opportunities for the teachers to examine new ideas within the contexts of their current practices and situations. To a certain degree this led to an increased focus on student learning, which in turn led to a gradually broadening view on what might constitute ‘student achievement’:

As the year progressed and the beginning teachers became more confident and competent with their work, new challenges emerged in their teachings that had not initially been apparent. These emerging issues began to act as key influences upon pedagogical beliefs and practices. They included: how to plan for mathematics instruction, isolation and lack of support within their professional practice, and the demands upon their personal lives.

All the beginning teachers had trouble with planning in that, as the year progressed, they expressed concerns that they lacked basic knowledge and skills for planning. For example, Harry noted: "When I first started I wasn’t all that confident at teaching mathematics. It didn’t do it on my ATP [Assistant Teacher Program]. I didn’t program for it, so I didn’t have any idea of where to start." The teachers looked for ready-made, short cut answers to planning so that the process would require relatively little time, and be simple and straight forward. A teacher-centred approach to teaching fulfilled these criteria, while at the same time acting in congruence with their beliefs about how mathematics ‘should’ be taught or their perceptions of what was expected in their schools:

The teachers’ inexperience in planning did not allow them to cater for multi-age and mixed ability classes. They had neither the skills nor confidence to adequately plan for and teach in ways that provided enriching learning experiences for all children. Further, they did not change substantially in this regard throughout the year, continuing (as has been mentioned earlier) to aim to keep the children ‘together’:

Except for Harry, the teachers were not offered any planning models or assistance within their schools. Harry was required to show his plans to the school principal, for which he sometimes received superficial, non-constructive feedback, while the others had no support from colleagues. They were just left to ‘get on with it’. This led to a feeling of isolation, the issue discussed next.

All the beginning teachers were placed in schools with experienced staff, yet they all came to feel as if they were alone in a crowd. It was noted in the interviews that when they first started at the schools other teachers would pop in and see if everything was okay, but these occurrences were merely friendly greetings and they did not continue as the year progressed. To compound this lack of explicit connections with others in the school, the beginning teachers generally felt they did not want to bother already busy colleagues with their beginning teaching problems. In addition, the beginning teachers did not want to be seen as inadequate, or unable to do the job:

The schools had no informal or formal support systems for new staff, and none of them had any explicit policies or procedures for induction of beginning teachers. There were some occasions when the beginning teachers had meetings with or worked alongside other teachers, but these were infrequent and did not focus on assisting the beginning teachers’ professional development. The ‘fellow worker’ was able to some degree to break the isolation, and through encouraging reflection, focus the teachers upon identifying areas of professional accomplishment and related feelings of success, rather than a focus upon problems and unresolved issues:

For all the teachers the challenges of adjusting to their new teaching situations while achieving balance with their personal lives was an ongoing endeavour that in some cases emerged as a major stress. These challenges varied between individuals, yet they all related to the impact of their work upon their family lives. Stephanie had to travel long distances to and from school each day, Tiffany found temporary accommodation and commuted home on weekends only, Harry had a young child and a wife hospitalised with complications in her second pregnancy, and Gaz had to manage wedding plans, getting married, and his house being burgled and vandalised. These extra and considerable challenges, coupled with the beginning teachers’ anxieties concerning time pressures, classroom control and syllabus coverage, made it difficult for the teachers to begin to consider taking risks and trying alternative pedagogical practices to those they initially adopted. That is, to survive while accommodating all these issues was a goal that influenced the ways they interpreted situations and any related actions.

The findings of this study highlighted the ‘survival’ stage that the beginning teachers passed through upon entering their first teaching placement (Katz, 1972). They faced situations that for them were challenging and demanding upon their professional knowledge, skills, and self-esteem. Further, they struggled in ongoing ways with aspects of classroom practice that they felt inadequately prepared to handle, and it appeared that they needed more professional support to assist their professional development towards learner-focused teaching. These general findings of the study point to three main things concerning teacher education and related research: